Question

A mass 2m lies on a fixed ,smooth cylinder. An ideal string attached to 2m passes over the cylinder to mass m. Then the value of angle $\theta$ for which the system is in equilibrium.

• A. ${40}_0$
• B. ${45}_0$
• C. ${60}_0$
• D. ${30}_0$

Answer 1

The correct option is D ${30}_0$

The correct option is D

Given,

$mass=2,length=2m,angle=\theta$

$FBD$ of $m$

$T-mg=0$

$T=mg$

Now $FBD$ of $2m$ is:

$2mgsin\theta =T$

$2mgsin\theta =mg$

$sin\theta =\frac{1}{2}$

$\theta =si{n}^{-1}\frac{1}{2}$

$={30}^0$